FRANKFURT (Reuters) - European Central Bank rate setters meeting last month opened the door to dropping a long-standing pledge to boost the ECB's bond-purchase program if necessary, minutes of the meeting showed on Thursday.

ECB policymakers discussed already taking out that so-called "easing bias" from their policy message at the June 7-8 meeting but decided against it because the euro zone's economic recovery had yet to result in higher inflation - the bank's main policy objective.

But, confirming a Reuters exclusive, the central bankers said they could review at future meetings the promise to increase the "size and/or duration" of its 2.3 trillion euro bond-buying program, if needed.

"If confidence in the inflation outlook improved further, the case for retaining this bias could be reviewed," the ECB said in its policy accounts.

German government bond yields hit new 18-month highs and the euro edged higher after the minutes were published.

With inflation in the euro zone slowly rebounding, the ECB is preparing to dial back its stimulus policy of ultra-low rates and massive bond purchases.

But doing so without upsetting investors is proving a challenge, with bond yields and the euro <EUR=> rising sharply last week after ECB President Mario Draghi hinted at possible policy tweaks.

"CONTINUED CAUTION"

In the minutes, the ECB stressed the need for "continued caution in communication" as any perception that it was moving away from its stimulus policy could upset financial markets, undoing some of its stimulus effort.

Indeed, ECB Chief Economist Peter Praet said earlier on Thursday the central bank needed to be patient and maintain a steady hand in policy as inflation was still far below its target of almost 2 percent.

Despite a brisk economic rebound, inflation in the euro zone was 1.3 percent in June and is not expected to near 2 percent at least until 2019.

ECB rate setters meeting in June said they found it "puzzling" that forecasts for core inflation had to be revised down despite stronger economic growth and a falling unemployment rate.

Still, Draghi argued last week that accelerating growth would in itself provide support so the ECB could tighten policy somewhat to keep the broad level of financial accommodation unchanged.

That message stirred markets, fuelling speculation that policymakers could decide as early as September to reduce asset purchases from next year.

The ECB's asset buys are set to run until the end of the year and policymakers will decide in September or October whether to extend, reduce or gradually wind down the purchases.